Question

Let ABC be a triangle and P be an interior point. Prove that AB + AC + CA < 2 (PA+PB+PC)

Answer 1

Given : ABC is a triangle where p is interior point.

To prove : AC+BC>AP+BP

Proof : In triangle ABC

angle A > angle PAB [ Whole is greater than a part ] ____(1)

angle B > angle PBA [ Whole is greater than a part ] _____(2)

On adding (1) and (2) we get

angle A + angle B > angle PAB + angle PBA

BC + AC > PB + AP [ Side opp. to respective angles ]

Or

AC + BC > AP + PB

Q.ED